1,720,982 research outputs found
A characterization of affine hyperquadrics
No full textIn this paper, using the existence of special exhaustions that satisfy the complex homogeneous Monge–Ampère equation and curvature properties are given characterizations of the affine hyperquadric and other special Stein manifolds
Monge-Ampere foliations with singularities at the boundary of strongly convex domains
Full text linkLet D subset of C-N be a bounded strongly convex domain with smooth boundary. We consider a Monge-Ampere type equation in D with a simple pole at the boundary. Using the Lempert foliation of D in extremal discs, we construct a solution u whose level sets are boundaries of horospheres. Among other things, we show that the biholomorphisms between strongly convex domains are exactly those maps which preserves our solution
UNIQUENESS OF COMPLEX GEODESICS AND CHARACTERIZATION OF CIRCULAR DOMAINS
No full textWe study complex geodesics for complex Finsler metrics and prove a uniqueness theorem for them. The results obtained are applied to the case of the Kobayashi metric for which, under suitable hypotheses, we describe the exponential map and the relationship between the indicatrix and small geodesic balls. Finally, exploiting the connection between intrinsic metrics and the complex Monge-Ampere equation, we give characterizations for circular domains in C(n)
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